ENVE5504 Surface Water Quality Modeling

Lab 2.Modeling Loads – The C/Q Approach Applied to Onondaga Lake

Types of Loads

load, mass·time-1, g·d-1

dCV W Q C V k Cdt

point source, tributaries: Q·C, m3·d-1 x g·m-3

nonpoint terrestrial source: UAL·A, g·m2·d-1 x m2

nonpoint atmospheric source: J·A, g·m2·d-1 x m2

sediment source: J·A, g·m2·d-1 x m2

What is “A” for the last 3 cases?

Steady State C, Constant Loads

dCV W Q C V k Cdt

and, at steady state,

ss

WC

Q V k

where W is constant and quantified as shown inthe previous slide.

Time Variable C, Time Variable Loads

dCV W Q C V k Cdt

applying numerical integration,

how to describe W(t) ?( )W t Q

dC C k C dtV V

Time Variable C, Idealized, Time Variable Loads

then an initial concentration is calculated,

and the integration proceeds with W = 0

( )W t m

Impulse load (spill)

0

mC

V

( )W t QdC C k C dt

V V

0

Time Variable C, Idealized, Time Variable Loads

where an initial concentration corresponding toprior conditions is specified

( ) newW t W

Step load (new continuous source)

0 ( )oldC f W

( )W t QdC C k C dt

V V

Time Variable C, Idealized, Time Variable Loads

where an initial concentration correspondingto prior conditions or Wbase is specified

( ) base lW t W t

Linear load

0 ( )baseC f W

( )W t QdC C k C dt

V V

Time Variable C, Idealized, Time Variable Loads

where an initial concentration correspondingto prior conditions or We is specified

( ) e teW t W e

Exponential load

0 ( )eC f W

( )W t QdC C k C dt

V V

Time Variable C, Idealized, Time Variable Loads

where an initial concentration correspondingto prior conditions or Wbar is specified

( ) sin( )bar aW t W W t

Sinusoidal load

0 ( )barC f W

( )W t QdC C k C dt

V V

The Clean Water Act and TMDLs

In 1972, the Federal Water Pollution Control Act was amended requiring, in part, a minimum level of control based on available treatment technologies. Where implementation of those technologies does not result in water quality standards being met, Section 303 of the Act requires that regulators,

Establish Total Maximum Daily Loads (TMDLs) for these waters at levels necessary to meet applicable water quality standards, accounting for seasonal variations and with a margin of safety to reflect lack of certainty about discharges and water quality.

This can be accomplished through a modeling approach where C represents the water quality standard and W represents the ‘necessary level’ of load, e.g.

dCV W Q C V k Cdt

Identifying Loading Sources

Example - Deer Lake, Michigan

sediments

tribs

WWTP

Characterizing and Quantifying Loads

load, mass·time-1, g·d-1

dCV W Q C V k Cdt

point source, tributaries: Q·C, m3·d-1 x g·m-3

nonpoint terrestrial source: UAL·A, g·m2·d-1 x m2

nonpoint atmospheric source: J·A, g·m2·d-1 x m2

sediment source: J·A, g·m2·d-1 x m2

Deer Lake Loads

load, mass·time-1, g·d-1

dCV W Q C V k Cdt

WWTP WWTP trib trib sed sedW Q C Q C J A

Consider challenges in quantifying these, e.g.

(1)accounting for seasonal variations and

(2)establishing a margin of safety

Quantifying Tributary Loads

( )W t Q C

( )tribQ f t USGS

( )tribC f t clueless

Approach: develop the relationship between C and Q, e.g.

as expressed in a C/Q plot. Apply that relationship to derive C values from the USGS Q data base and then use W(t) = Q·C to calculate the load.

C a Q b

a

bC

Q

C/Q for TSS in Ontonagon River, Lake Superior

• linear• bipartite• ascending - descending

C/Q for Chloride in Nine Mile Creek, Onondaga Lake

• inverse linear plot • two different historical intervals

C/Q for TSS in Onondaga Creek, Onondaga Lake

• logC plot

C/Q for Total Phosphorus in Onondaga Creek, Onondaga Lake

• log – log plot• two different stations

Regression Analysis of Maumee River Phosphorous Loading Data Water Years 2003-2005

Charlie Piette and David Dolan

Pete Richards

National Center for Water Quality Research Heidelberg College

Department of Natural and Applied SciencesUniversity of Wisconsin Green Bay

Maumee River Facts

• Size

• Contribution

Seek a Concentration/Flow Relationship

- 3. 5

- 3. 0

- 2. 5

- 2. 0

- 1. 5

- 1. 0

- 0. 5

0. 0

LnFl ow

4 5 6 7 8 9 10 11 12

C

Q

Little loads, like those from toads,Grow bigger when from horses.And on through us, I fear they must,Foul the water courses.

Ode to the Load